Sophismata

In contrast to the meaning the word ‘sophism’ had in
ancient philosophy, ‘sophisma’ in medieval
philosophy is a technical term with no pejorative connotation: a
sophisma is an ambiguous, puzzling or simply difficult
sentence that has to be solved. As an important element of scholarly
training in universities, closely related to different kinds of
disputations, the sophismata not only served to illustrate a
theory but, from a more theoretical point of view, were also used to
test the limits of a theory. The so-called
sophismata-literature assumed more and more importance during
the thirteenth and fourteenth centuries, and it is not an exaggeration
to claim that many important developments in philosophy (mainly in
logic and natural philosophy) appeared in texts of this kind, where
masters could feel free to investigate problems and develop their own
views, much more than they could in more academic and strictly codified
literary genres.

Although some medieval theologians — and Humanists even more, of
course, like Vivès or Rabelais — used the words
‘sophism’ or ‘sophist’ as a derogatory
designation for quibbling philosophers, ‘sophisma’
in medieval philosophical literature has a very precise and technical
signification. Hence, to avoid any confusion with fallacies and
badly-constructed arguments, we shall here use the original term
‘sophisma’ rather than the word
‘sophism’ that even nowadays still has a pejorative
connotation.

Once the odd, ambiguous or puzzling sophisma-sentence is put
forward, one should try to understand what it means, what implications
it has, and how it fits into or contradicts a particular theory under
consideration. This is called “solving
the sophisma,” and is the aim of the entire
discussion. The way solutions are searched for and established is very
similar to the highly formalized scholastic method for determining a
“question”:

First, one has to examine the arguments pro and
contra.

Second, one has to present his own solution to the problem.
(Sometimes this part of the discussion is preceded by certain
theoretical remarks or clarifications that make the terminology more
precise.)

Third, one has to refute the arguments supporting the opposite
answer.

An Example

Let us take a very simple example, from Albert of Saxony,
Sophismata, sophisma xi. The sophisma is:

Omnes homines sunt asini vel homines et asini sunt
asini.
(All men are donkeys or men and donkeys are donkeys.)

In accordance with step (1), here are the pro and
contra arguments:

Proof: The sophisma is a copulative sentence (in
modern logical terminology, a conjunction) each part of which is true;
therefore the sophisma is true, since its analysis becomes:
[All men are donkeys or men] and [donkeys are donkeys].

Disproof: The sophisma is a disjunctive sentence each part
of which is false; therefore the sophisma is false, since its
analysis becomes: [All men are donkeys] or [men and donkeys are
donkeys].

This is a sophisma of the second kind above, one that rests on
an ambiguity and can be read with a true interpretation or with a false
interpretation. Many such sophismata, although not this one,
resist being translated from Latin into another language without losing
the ambiguity. For example, the sentence ‘aliquem asinum omnis
homo videt’ can be translated by ‘Every man sees a
donkey’ as well as by ‘There is a donkey that every man
sees’. Similarly, in solving sophismata, sometimes Latin
word-order is used as an arbitrary code for interpreting the sentence.
For example, according to William Heytesbury, when the word
‘infinite’ is placed at the beginning of a sentence and
belongs to the subject, it has to be interpreted as a syncategorematic
term; in any other case, it is usually interpreted as a categorematic
term (Heytesbury, Sophismata, sophisma xviii,
fol.130va). Such word-order codes might seem like reasonable
regimentations of language to a Latin-speaker, but in translation they
often seem quite implausible and forced. No such problems arise with
this example. (For clarity, square brackets have been inserted into the
proof and disproof above, in order to indicate the ambiguity of the
sophisma.)

In accordance with step (2) above, Albert of Saxony, who discusses
this sophisma, solves it by just saying that it is either true
or false depending on which interpretation we choose. He then takes the
opportunity to review the basic principles governing the truth-value of
copulative and disjunctive sentences.

In accordance with step (3), we would normally be required to refute
the opposite answer. In this case, however, there is nothing to refute,
since Albert's solution accepts both the pro and the
contra arguments (for different readings of the
sophisma).

In general, a sophisma was a good occasion to discuss all the
problems related to a specific issue. For example, the
sophisma ‘Album fuit disputaturum’
(‘The white [thing] was about to dispute’) in
thirteenth-century Parisian literature was the occasion to discuss all
the problems related to the theory of reference in tensed contexts, as
well as to refute the positions others held on this very controversial
subject. This is why Pinborg 1977 (p. xv) says that at Paris in the
thirteenth century “the sophismata seems — within the
faculty of arts — to play a role analoguous to the
Quaestiones quodlibetales [quodlibetal questions] in the
faculty of theology.” Note that this use is quite common. (Note also
that Pinborg here uses the word ‘sophismata’ to
signify not only sophisma-sentences but the whole literature
that discussed them as well.)

Syncategorematic Terms, Exponible Sentences

It is important to recognize that many sophismata involve
syncategorematic terms that are responsible for their odd, ambiguous or
puzzling character. The preceding sophisma can be considered
quite characteristic of the genre insofar as we see that the
syncategorematic terms ‘or’ and ‘and’ occur in
it and are responsible for the ambiguity of the sentence.

The expression ‘syncategorematic term’ should be taken in
a broad sense here, so that it not only includes classical
syncategorematic terms like ‘and’, ‘if’,
‘every’, etc., but also categorematic terms like
‘infinite’ or ‘whole’ that can be used both
categorematically and syncategorematically. Thus the sentence
“Infinita sunt finita” (“The infinite are
finite” — here, incidentally is another good example of
a sophisma that cannot be translated into English without
disambiguating it) is false if ‘infinite’ is used
categorematically, for in that case its signification is “Things
that are infinite are finite.” But it is true if
‘infinite’ is used syncategorematically, for in that case
its signification is “Finite things are infinite in
number” or “There are infinitely many finite
things.” (See Heytesbury,
Sophismata,sophisma xviii, fol.130va.)

Many sophismata too are what medieval logicians called
“exponible sentences”, sentences that seem to be simple but actually
imply several other sentences into which they can be decomposed. For
example, the sentence “A differs from B” was said to be
equivalent to “A exists and B exists and A is not
B”; the sentence “A ceases to be white” was said to be
equivalent either to “Now A is white and immediately after this
A will not be white” or to “Now A is not white and
immediately before this A was white”, depending on the
theory.

Just as the scholastic method can be applied to any subject, the use of
sophismata is to be found in logic, grammar and physics as
well as in theology. Let us concentrate here on the first three.

Logical Sophismata

As seen above, logical sophismata are closely linked to the
discussions of syncategoremata. The aim is either to determine the
truth-value of a sentence (including sentences involving
self-reference) or to discuss subjects such as:

The syntactic and semantic properties of terms (including the
difference between meaning and reference) in sentences like
“Every man sees every man,” “You are a
donkey,” and “I promise you a horse.”

Quantification and existential import, as in the sentence “Every
phoenix is.”

The theory of negation and “infinite” words, as in the sentence
“Nothing and a chimaera are brothers.”

The problem of universals, as in “Man is a species.”

The composite and divided senses of a sentence and the scope of
modal operators, as in “The white can be black,”
“Every man is of necessity an animal,” etc.

We could compare these discussions to contemporary discussions of
sentences like “The morning star is the evening star.”

Physical Sophismata

The aim here is to discuss physical concepts (motion, change, velocity,
intension and remission of forms, maxima and minima, etc.). But, as
seen above with the sophisma “The infinite are finite,”
physical problems are treated as logical and conceptual problems. This
logico-semantical approach to physical problems is quite characteristic
of medieval physics and should be kept in mind when we wonder the
extent to which medieval physics can be considered a precursor to
modern physics.

With respect to so-called physical sophismata, special
attention should be paid to certain fourteenth century English
authors known as the “Oxford Calculators,” authors like
Richard Kilvington, William Heytesbury, Thomas Bradwardine, Richard
and Roger Swineshead. These people developed a peculiarly
“English-style” of
sophismata. Based on the theological dogma of the absolute
power of God, the distinction between what is physically possible and
what is logically possible (where non-contradiction is the only limit)
allowed these authors to make use of imaginary thought experiments. For
example, “Suppose that A is a distance to be traversed which
Socrates cannot traverse, and that his power is increased until
Socrates can traverse distance A completely, and that Socrates'
power is not increased further.” Is the sophisma “Socrates
will begin to be able to traverse distance A” true or false?
(Richard Kilvington, Sophismata,sophisma 27, in
Kretzmann 1990, p.60.) Thought experiments like these led these authors
to, among other things, a theorem for uniformly accelerated motion
(Thomas Bradwardine's “Mean Speed Theorem”).

Grammatical Sophismata

Sophismata like “Love is a verb,” “O
Master,” “It rueth me” or “I run” gave
rise to very sharp discussions of grammatical categories and
theories. For example, does a change of word order change the meaning
of a proposition? Can a participle be a subject? How should we
interpret interjections? Can ‘est’
(“is”) be used impersonally?

The first and most evident role of sophismata is pedagogical.
In theoretical treatises, sophismata can play various roles.
They can be used to explain a given statement or rule, illustrate a
distinction or an ambiguity, show what would follow if a rule were
violated, or test the limits of a theory.

In addition, although some differences can be identified between the
Paris and the Oxford traditions, sophismata are important as
oral exercises (disputations) in a student's training in philosophy,
especially in the first years of universitary education in the Faculty
of Arts. Nevertheless, it is clear that, while Heytesbury's Rules
for Solving Sophismata is written for undergraduate students
— at Oxford ‘sophista’ was the official
name given to students who had disputed “on sophismata”
(“de sophismatibus”) for about two years — this is
probably not the case for his Sophismata, the discussions in
which are much more complicated.

I think it is no exaggeration to say that sophismata in the
Faculty of Arts were as important as Biblical exegesis in the Faculty
of Theology.

If we look at the evolution of literary genres, we note that the
twelfth- and early-thirteenth century
syncategoremata-literature came to be absorbed in the
sophisma-literature. In thirteenth and fourteenth century
philosophical literature, sophismata can appear within many
kinds of treatises. Besides in syncategoremata-treatises,
sophismata are dealt with in separate collections of
sophismata named simply Sophismata or On
Sophismata, but they also play an important role in general
manuals of logic, and in works — often by the same authors, or
by different authors coming from the same milieu as the former
collections — with titles like Abstractions,
Distinctions,On Exponibles,On
Consequences,Sophistry, etc.

Even if there are technical distinctions among these types of
tracts, all of them play the same roles mentioned above — in
short: to acquire logical skills that can be applied to any
subject.

The medieval sophismata-literature is a vast and complex
subject of research. Many questions are still unsolved, especially
about its historical origins and development. It is of central interest
for people interested in medieval logic, grammar and physics, but also
for those interested in the history of universities.

The study of “sophismatic works” began around 1940 with Grabmann's
Die Sophismatalitteratur des 12. und 13. Jahrhunderts, and
much work has been done in the last two decades. Recently a
comprehensive catalogue of 13th century sophismata has been
published. But there are still a lot of texts to read, edit and
analyze.

Most of the logical and grammatical texts on sophismata have
been edited by S. Ebbesen and his collaborators in the review
Cahiers de l'Institut du Moyen Age Grec et Latin,
University of Copenhagen. We will here mention only
books.

Longeway, J. William Heytesbury: On Maxima and Minima. Chapter
5 of ‘Rules for Solving Sophismata’, with an Anonymous
Fourteenth Century Discussion, a Translation with an Introduction and
Study. Synthese Historical Library, 26; Dordrecht: Reidel,
1984.

Hughes, G. E. John Buridan on Self-Reference. Chapter Eight of
Buridan's ‘Sophismata’. An Edition and a Translation with
an Introduction and a Philosophical Commentary. Cambridge:
Cambridge University Press, 1982. (The paperbound edition omits the
Latin text.)

Many important studies are to be found in the following collective
work: S. Read (ed.), Sophisms in Medieval Logic and Grammar (Acts
of the Ninth European Symposium for Medieval Logic and Semantics, St.
Andrews, June 1990), Dordrecht: Kluwer Academic Publishers, 1993.

Kretzmann, N., 1982, “Syncategoremata, exponibilia,
sophismata,” in N. Kretzmann, et al. (eds.), The
Cambridge History of Later Medieval Philosophy from the Rediscovery of
Aristotle to the Disintegration of Scholasticism, 1100-1600,
Cambridge: Cambridge University Press, 211-45.

Kretzmann, N., 1982, “Continuity, Contrariety, Contradiction
and Change,” in N. Kretzmann (ed.), Infinity and Continuity
in Ancient and Medieval Thought (Papers Presented at a Conference
held at Cornell University on April 20 and 21 1979, under the Title
‘Infinity, Continuity and Indivisibility in Antiquity and the
Middle Ages’), Ithaca: Cornell University Press,
322-40. (Appendix: “Text of Walter Burleigh and the Sophisms 8
and 16 of Richard Kilvington.”)

Murdoch, J. E., 1982, “Infinity and Continuity,” in
N. Kretzmann, et al. (eds.), The Cambridge History of
Later Medieval Philosophy from the Rediscovery of Aristotle to the
Disintegration of Scholasticism, 1100-1600, Cambridge: Cambridge
University Press, 564-91.